# Sylvester's Problem and Mock Heegner Points

@article{Dasgupta2017SylvestersPA,
title={Sylvester's Problem and Mock Heegner Points},
author={Samit Dasgupta and John Voight},
journal={arXiv: Number Theory},
year={2017}
}
• Published 18 July 2017
• Mathematics
• arXiv: Number Theory
We prove that if $p \equiv 4,7 \pmod{9}$ is prime and $3$ is not a cube modulo $p$, then both of the equations $x^3+y^3=p$ and $x^3+y^3=p^2$ have a solution with $x,y \in \mathbb{Q}$.

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